generation in s uperparamagnetic particles Christian Moerland LeoJ van IJzendoorn MennoWJ Prins cpmoerlandtuenl Assumptions and model for the grains The MSPs grains have a size distribution based on previous work we assume this is a ID: 252503
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Slide1
On
torque generation in superparamagnetic particlesChristian Moerland*, Leo.J. van IJzendoorn, Menno.W.J. Prins* c.p.moerland@tue.nl
Assumptions and model (for the grains)
The MSP’s grains have a size distribution, based on previous work we assume this is a log-normal distribution. The grains have an anisotropy axis, if the magnetization is not aligned with this axis the energy cost is given by the Stoner-Wohlfarth energy. The grains are small and there magnetic orientation is dominated by thermal fluctuations. The typical time it takes to flip is given by the Néel relaxation time.We take two axes in consideration for the particles magnetic behavior these axes are parallel to: external magnetic field and the anisotropy axis of a single grain.
Background and AimThe torsion properties of proteins and DNA have been studied on the single-molecule level using multicore magnetic particles[1-2]. These multicore super-paramagnetic particles (MSP) consist of multiple (106) single domain ferromagnetic grains with a radius of a few nanometer encapsulated in a polystyrene shell. Due to the size of the grains their behaviour is dominated by thermal fluctuations. The aim of the project is to construct a framework to explain the magnetic behavior of the MSP, to understand the mechanism of torque generation and categorize the different types of commercially available particles.
What we found (for a particle):For fields < 100mT grains almost only magnetize over their easy axes.All grain sizes can contribute to the torque, not just the largest. No torque for very small field ()Decrease in the torque for large fields () Torque requires a non uniform distribution of the anisotropy axes In equilibrium () the maximum phase lag is (and for ())
/ department of applied physics
Outlook
We will test this model by experimentally constructing the (
B,Hz)-plane as in figure 4. This will be done by a protein torsion experiment like in figure 3 (right) and will be look at the maximum angular displacement of the peak corresponding to the double frequency relative to the peak corresponding to the field frequency . This can be done by defining as the the relative height difference of the peaks in around and in the Fourier spectrum.This will be done for different commercially available MSP (M-270, M-280, MyOne…) to get information about their internal structural differences.
Steps (
grain to particle):1) Assume the grains remagnetize between discrete directions2) Remagnetisation along the easy axis3) Alignment along the external field or the easy axis4) Solve for equilibrium ()5) Integrate over grain size distribution for total magnetization of the particle is the, normalized, portion of the time the grain is magnetization over an axes ( or ) is a attempt frequency
Transition from 90 to 45 deg.
m
ax. phase lagsIn previous torsion experiments we saw that the system went from a frequency mode equal to the applied field to twice that if the field was large enough (flipping). This was explained by discrete flipping of large grains.
The probability for
remagnetization in a rotating field depends on the magnitude and angular frequency of the applied field.
The phase angle at which the MSP
remagnetizes is given by where is defined as the time it takes to remagnetize (so ) but has to be smaller than (time it takes for the field to rotate 90deg). We see a strong size dependence if we solve the for .
Figure 2: A schematic representation of the grains magnetization and the torque induced. Top a non flipping grain and Bottom a flipping grain.
Flipping
Non Flipping
Figure 4: Plots of the probability for
remagnetization
in the B-Hz plane for grain sizes of 7.4nm and 7.6nm.
Radius: 7.6
nm
Radius: 7.2
nm
Figure 1: Left: A SEM image of a MSP (M-270). Middle: A sketch of the cross-section showing the single domain ferromagnetic grains. Right: The two importuned axis for magnetization of a grain
[1] A
. v. Reenen, F. Gutierrez Mejia, L.J. van
IJzendoorn
, M.W.J. Prins,
Biophys. J. 104 (2013) 1073-1080[2] F. Mosconi, J. F. Allemand, D. Bensimon, and V. Croquette, Phys. Rev. Lett. 102 (2009) 078301[3] L.J.P. Verhees, F. Gutierrez Mejia, L. J. nan IJzendoorn, Graduation report.
Figure 3: The angular rotation of a molecular spring for different fields. Dots are measurements lines are simulations
[3]
B
A
C
5mT, 0.4Hz
10mT,
0.2Hz 20mT, 0.4Hz